Lightroom where you can very easily output at the native resolution regardless of the desired print dimension...
In practice though I would never downsample merely to hit some sort of output resolution. Why waste the pixels?
There can be reasons to downsample, but it depends on the situation. When the downsampling factor is significant, and the subject in the image is sensitive to the creation of aliasing artifacts, and the output modality doesn't dither or anti-aliase the result enough, then it's beneficial to do a correct downsampling before sensing the data to the print driver's 'black box' (bi-linear?) downsampling algorithm. Granted, a lot of conditions need to be met. A simple print test with a critical image can tell whether one runs a risk. Another reason can be to reduce the amount of print data, e.g. when printing over a network or when the spoolfile can get too large in a large batch printjob that has to run unattended.
Upsampling "can" help the output if you A) do it well and do proper sharpening after the upsample...
That's correct, it has to be done well (i.e. not introduce artifacts in the process, and possibly create useful extra data), and
a huge benefit is that sharpening can be done at the final print resolution which is more precise and gives less chance of creating sharpening artifacts. This does assume proper interpolation to the native printer (driver) resolution for a given paper type.